Method and system for characterization of subsurface cavities using joint inversion of gravity and ground penetrating radar data
View Patent ↗A system and associated methodology determines the porosity and water saturation of a cavity using a joint inversion of gravity and ground penetrating radar data. The system exhibits high accuracy. In one embodiment, the cavity is spherical.
1. A method for characterizing subsurface cavities, the method comprising:
receiving, via a network, ground penetrating radar measurements in a radiowave band from a ground penetrating radar device storing physical constants;
receiving, via the network, gravity measurements;
calculating, using processing circuitry, a porosity of cavity filling materials based on the ground penetrating radar measurements and the gravity measurements using a data inversion approach;
calculating a water saturation of the cavity filling materials based on the ground penetrating radar measurements and the gravity measurements using the data inversion approach;
sending the porosity and the water saturation to an external device to provide geological characterizing of the subsurface cavities to host applications; and
drilling in a location based on the calculated porosity and the water saturation.
2. The method of claim 1 , wherein the subsurface cavities are spherical.
3. The method of claim 2 , further comprising:
calculating the porosity as a function of a half width of a gravity anomaly curve, a travel time from ground surface to bottom of a host layer through center of the cavity, an electromagnetic wave velocity through the host layer, a distance from ground surface to the top of the cavity, a thickness of the host layer, densities of the cavity filling materials and permittivities of the cavity filling materials.
4. The method of claim 3 , wherein the porosity is calculated using
ϕ
=
CM
-
AD
CN
-
BD
where
A
=
1.27
(
x
1
/
2
)
2
g
max
π
G
(
1.305
x
1
/
2
-
H
s
1
)
3
+
ρ
s
-
ρ
g
,
B
=
ρ
a
-
ρ
g
,
C
=
ρ
w
-
ρ
a
,
D
=
ɛ
w
-
ɛ
a
,
M
=
0.3
(
v
s
T
c
-
2
H
s
+
4
(
1.305
x
1
/
2
-
H
s
1
)
)
4
v
s
(
1.305
x
1
/
2
-
H
s
1
)
-
ɛ
g
and
N
=
ɛ
a
-
ɛ
g
where x 1/2 is the half-width of the anomaly curve, g max is the maximum gravity anomaly, G is the universal gravitational constant, ρ s , ρ g , ρ a , ρ w , ∈ a , ∈ w , and ∈ g are geophysical constants, v s is the velocity, T c is the travel time, and H s and H s1 are constants.
5. The method of claim 3 , wherein the densities of the cavity filling materials and the permittivities of the cavity filling materials are stored in a memory.
6. The method of claim 5 , wherein the water saturation is calculated using
S
w
=
-
BM
+
AN
CN
-
BD
where
A
=
1.27
(
x
1
/
2
)
2
g
max
π
G
(
1.305
x
1
/
2
-
H
s
1
)
3
+
ρ
s
-
ρ
g
,
B
=
ρ
a
-
ρ
g
,
C
=
ρ
w
-
ρ
a
,
D
=
ɛ
w
-
ɛ
a
,
M
=
0.3
(
v
s
T
c
-
2
H
s
+
4
(
1.305
x
1
/
2
-
H
s
1
)
)
4
v
s
(
1.305
x
1
/
2
-
H
s
1
)
-
ɛ
g
and
N
=
ɛ
a
-
ɛ
g
where x 1/2 is the half-width of the anomaly curve, g max is the maximum gravity anomaly, G is the universal gravitational constant, ρ s , ρ g , ρ a , ρ w , ∈ a , ∈ w , and ∈ g are geophysical constants, v s is the velocity, T c is the travel time, and H s and H s1 are constants.
7. The method of claim 2 , further comprising:
calculating the water saturation as a function of a half width of a gravity anomaly curve, a travel time from ground surface to bottom of a host layer through center of the cavity, an electromagnetic wave velocity through the host layer, a distance from ground surface to the top of the cavity, a thickness of the host layer, densities of the cavity filling materials and permittivities of the cavity filling materials.
8. The method of claim 7 , wherein the densities of the cavity filling materials and the permittivities of the cavity filling materials are stored in a memory.
9. The method of claim 1 , wherein the ground penetrating radar measurements are used without calculating a velocity tomogram.
10. A system for characterizing subsurface cavities, the system comprising:
a ground penetrating radar device;
a microgravity survey device; and
processing circuitry configured to:
receive, via a network, ground penetrating radar measurements from the ground penetrating radar device in a radiowave band from a ground penetrating radar device storing physical constant,
receive, via the network, gravity measurements from the microgravity survey device,
calculate a porosity of cavity filling materials based on the ground penetrating radar measurements and the gravity measurements using a data inversion approach,
calculate a water saturation of the cavity filling materials based on the ground penetrating radar measurements and the gravity measurements using the data inversion approach,
send the porosity and the water saturation to an external device to provide geological characterizing of the subsurface cavities to host applications, and
drill in a location based on the calculated porosity and the water saturation.